Question: Solve for $x$ and $y$ using elimination. $\begin{align*}4x-2y &= -8 \\ -x+9y &= 2\end{align*}$
Explanation: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $1$ and the bottom equation by $4$ $\begin{align*}4x-2y &= -8\\ -4x+36y &= 8\end{align*}$ Add the top and bottom equations. $34y = 0$ Divide both sides by $34$ and reduce as necessary. $y = 0$ Substitute $0$ for $y$ in the top equation. $4x-2( 0) = -8$ $4x = -8$ $4x = -8$ $x = -2$ The solution is $\enspace x = -2, \enspace y = 0$.